Chabad does not read any Meggilos except for Eicha and Esther.
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Shmuel BrinMay 30 '12 at 17:19

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@yoel I just saw that the Lubavitcher Rebbe says (in the sicha of the second day of Shavuos 5717) that we don't say Akdamus because if someone understands the greatness of Hashem, how lofty he is, and how lofty is the Torah that comes from Him, saying Akdamus may permit one to focus on the "Gilyuim" rather that on Hashem's essence.
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Shmuel BrinAug 14 '12 at 22:50

2 Answers
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Only Ashkenazic communities read all five megillos in a public setting over the course of the year. Sefardic and Chassidic communities generally will only read Eicha on Tisha B'av and (of course) Esther on Purim, but not the other three on the shalosh regalim.

The custom to read Ruth on Shavuos (as well as Shir Hashirim on Pesach, I think) is mentioned earliest in Maseches Sofrim (14:18) (although the custom of exactly when during the holiday to say it is not the same). Many reasons are given for each megilla for why it is read on its corresponding holiday, but as far as I know, those are found in more recent works.

Some sepharadim read Ruth in public before mincha of Yom tov. They use to separate it in two parts for the two days outside Erets Israel. This is the case in France for Jewish from North Africa.
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allcedMay 31 '12 at 12:33

That only says "in many synagogues it is read publicly." As Alex said the part that "The Book of Ruth is recited as part of the program of study for Shavuot night" is the Chabad practice.
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YishaiNov 18 '13 at 23:08